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Question

Physics Question on potential energy

The energy stored in the electric field produced by a metal sphere is 4.5 J4.5\, J. If the sphere contains 4 μC 4 \, \mu C charge, its radius will be : [Take : 14πϵo=9×109 N−m2/C2\frac{1}{4 \pi \epsilon_o } = 9 \times 10^{9} \, N - m^2 / C^2 ]

A

20 mm

B

32 mm

C

28 mm

D

16 mm

Answer

16 mm

Explanation

Solution

Energy of sphere = Q22C\frac{Q^{2}}{2C} 4.5=16×10−122C4.5 = \frac{16\times10^{-12}}{2C} C=16×10−129=4πε0RC = \frac{16\times10^{-12}}{9} = 4\pi\varepsilon_{0}R R=16×10−129×14πε0R = \frac{16\times10^{-12}}{9}\times\frac{1}{4\pi\varepsilon_{0}} =9×109×169×10−12= 9\times10^{9}\times\frac{16}{9}\times10^{-12} =16??10−3=16mm= 16 ??10^{-3} = 16 mm